Question

in the circle given below O is its centre and lengths of the chord AB and CD are in the ratio 5:3.If angle AOB=100,find angle COD​

Answer 1

Given : O is its centre and lengths of the chord AB and CD are in the ratio 5:3

angle AOB=100

To Find : angle COD

Solution:

OA = OB = OC = OD  = Radius = R

AB²  = OA²  + OB² - 2OA.OBCos∠AOB

=> AB² = R² + R² - 2R²Cos100°

=> AB² = 2R² - 2R²Cos100°

=> AB² = 2R²  (1 - Cos100°)

=> AB² = 2R²2Sin²50°

=> AB  = 2RSin50°

CD   = 2RSin(∠COD/2)

AB : CD = 5 : 3

=> 5/3  = 2RSin50° /  2RSin(∠COD/2)

=> Sin(∠COD/2) = 3 Sin50° / 5

=>  Sin(∠COD/2) = (3/5)(0.766)

=> Sin(∠COD/2) = 0.4596

=> ∠COD/2 = 27.36°

=> ∠COD = 54.72°

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